Changed how the Visited nodes are tracked (#3811)

Updated the code to track visited Nodes with Set data structure instead of Lists to bring down the lookup time in visited  from O(N) to O(1)
as doing O(N) lookup each time in the visited List will become significantly slow when the graph grows

graphs/bfs_shortest_path.py

@@ -1,8 +1,6 @@
 """Breadth-first search shortest path implementations.
-
     doctest:
     python -m doctest -v bfs_shortest_path.py
-
     Manual test:
     python bfs_shortest_path.py
 """
@@ -19,22 +17,19 @@ graph = {
 
 def bfs_shortest_path(graph: dict, start, goal) -> str:
     """Find shortest path between `start` and `goal` nodes.
-
     Args:
         graph (dict): node/list of neighboring nodes key/value pairs.
         start: start node.
         goal: target node.
-
     Returns:
         Shortest path between `start` and `goal` nodes as a string of nodes.
         'Not found' string if no path found.
-
     Example:
         >>> bfs_shortest_path(graph, "G", "D")
         ['G', 'C', 'A', 'B', 'D']
     """
     # keep track of explored nodes
-    explored = []
+    explored = set()
     # keep track of all the paths to be checked
     queue = [[start]]
 
@@ -61,7 +56,7 @@ def bfs_shortest_path(graph: dict, start, goal) -> str:
                     return new_path
 
             # mark node as explored
-            explored.append(node)
+            explored.add(node)
 
     # in case there's no path between the 2 nodes
     return "So sorry, but a connecting path doesn't exist :("
@@ -69,16 +64,13 @@ def bfs_shortest_path(graph: dict, start, goal) -> str:
 
 def bfs_shortest_path_distance(graph: dict, start, target) -> int:
     """Find shortest path distance between `start` and `target` nodes.
-
     Args:
         graph: node/list of neighboring nodes key/value pairs.
         start: node to start search from.
         target: node to search for.
-
     Returns:
         Number of edges in shortest path between `start` and `target` nodes.
         -1 if no path exists.
-
     Example:
         >>> bfs_shortest_path_distance(graph, "G", "D")
         4
@@ -92,7 +84,7 @@ def bfs_shortest_path_distance(graph: dict, start, target) -> int:
     if start == target:
         return 0
     queue = [start]
-    visited = [start]
+    visited = set(start)
     # Keep tab on distances from `start` node.
     dist = {start: 0, target: -1}
     while queue:
@@ -103,7 +95,7 @@ def bfs_shortest_path_distance(graph: dict, start, target) -> int:
             )
         for adjacent in graph[node]:
             if adjacent not in visited:
-                visited.append(adjacent)
+                visited.add(adjacent)
                 queue.append(adjacent)
                 dist[adjacent] = dist[node] + 1
     return dist[target]